Name Period Date. Measurements. Fill-in the blanks during the PowerPoint presentation in class.

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1 Name Period Date Measurements Fill-in the blanks during the PowerPoint presentation in class. What is Scientific Notation? Scientific notation is a way of expressing big numbers and small numbers. It is most often used in scientific calculations where the analysis must be very. For very large and very small numbers, notation is more concise. Scientific notation consist of two parts: A number between A power of N x 10 x To change standard form to scientific notation Move decimal point to place after the non-zero digit Count the number of decimal places the decimal point has moved from the original number. This will be the on the 10. If the original number was less than 1, then the exponent is. If the original number was greater than 1, then the exponent is. Example: Given: 289,800,000 Given: Use: (moved 8 places) Use: 5.67 (moved 4 places) Answer: Answer: To change scientific notation to standard form Simply move the decimal point to the for positive exponent 10. Move the decimal point to the for negative exponent 10. (Use to fill in places.) Example: Given: x 10 6 Given: x 10-4 Answer: Express these numbers in Scientific Notation: 1) ) ) ) 2 5) Answer: Types of Observations and Measurements We make observations of reactions changes in color and physical state. We also make observations, which involve numbers. Use based on the metric system SI Measurements (Le Systéme international d unités) 1

2 Stating a Measurement In every measurement there is a 1) followed by a 2) from a measuring device The number should also be as precise as the measurement! Unit of Measurement Use SI units based on the metric system Length Mass Volume Time Temperature Match L) length M) mass V) volume A. B. C. D. A bag of tomatoes is 4.6 kg. A person is 2.0 m tall. A medication contains 0.50 g Aspirin. A bottle contains 1.5 L of water. Metric Prefixes Prefixes are added to units of measurements. They can represent of the base. (ex. 1 kilogram = g) Or they can represent of the base. (ex. 1 centimeter = meter) Units of Length kilometer (km) = 500 meters (m) 2.5 meter (m) = centimeters (cm) 1 centimeter (cm) = millimeter (mm) 1 nanometer (nm) = 1.0 x 10-9 meter Select the best answer m = 1 a) mm b) km c) dm g = 1 a) mg b) kg c) dg L = 1 a) ml b) cl c) dl m = 1 a) mm b) cm c) dm 2

3 Reading a Ruler First digit (known) = Second digit (known) = Third digit (estimated) = Length reported = Known + Estimated Digits In 2.33 cm Known digits 2 and 3 are 100% The third digit 3 is estimated ( ) In the reported length, all three digits (2.33 cm) are including the estimated one Zero as a Measured Number What is the length of the line at A? : What is the measurement at First digit cm line B? Second digit cm How does your answer compare with your Last (estimated) digit is cm neighbor s answer? Significant Figures The numbers reported in a measurement are by the measuring tool Significant figures in a measurement include the known digits plus one digit Counting Significant Figures Ex. No. of SF RULE 1. All non-zero digits in a measured number are significant cm 4 Only a zero could indicate that rounding occurred. 5.6 ft lb Leading Zeros m RULE 2. Leading zeros in decimal numbers are NOT significant mm oz lb Sandwiched Zeros ml RULE 3. Zeros between nonzero numbers are significant mm 3 (They can not be rounded unless they are on an end of a number.) 2001 min lb Trailing Zeros m RULE 4. Trailing zeros in numbers without decimals are NOT significant. 25,000 in 2 They are only serving as place holders yr 3 48,600 25,005,000 g 3

4 1. Which answers contain 3 significant figures? a) b) c) All the zeros are significant in a) b) c) x ,675 rounded to 3 significant figures is a) 535 b) 535,000 c) 5.35 x 10 5 Significant Numbers in Calculation A calculated answer be more precise than the measuring tool. A calculated answer must match the precise measurement. Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing 4. In which set(s) do both numbers contain the same number of significant figures? a) 22.0 and b) and 40 c) and 150, State the number of significant figures in each of the following: A m B L C g D m E. 2,080,000 bees Adding and Subtracting The answer has the same number of decimal places as the measurement with the decimal places decimal place decimal places answer 26.5 decimal place In each calculation, round the answer to the correct number of significant figures = a) b) c) = a) b) c) 40.7 Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the significant figures. Ex: = SF SF round to lowest ( SF) Equalities State the same measurements in two different units length X 4.2 = a) 9 b) 9.2 c) = a) b) 62 c) X = X a) 11.3 b) 11 c) in 2.54 cm 4

5 Conversion Factors Fractions in which the numerator and denominator are quantities expressed in different units Example: 1 in. = 2.54 cm Factors: Write conversion factors that relate each of the following pairs of units: 1. Liters and ml 2. Hours and minutes 3. Meters and kilometers Sample Problems: 1) How many minutes are in 2.5 hours? By using dimensional analysis/ factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers! 2) You have $7.25 in your pocket in quarters. How many quarters do you have? How many seconds are in 1.4 days? Unit plan: English and Metric Conversion If you know ONE conversion for each type of measurement, you can convert anything! Use these conversions: Mass: 454 grams = 1 pound Length: 2.54 cm = 1 inch Volume: L = 1 quart An adult human has 4.65 L of blood. How many gallons of blood is that? Your Setup: 5

6 Steps to Problem Solving problem Identify data Make a unit from the initial unit to the desired unit Select Change initial unit to desired unit Do math on calculator Give an answer using Temperature Scales Notice that 1 kelvin = 1 degree Density- an important and useful property Density = Density is an property of matter. does NOT depend on quantity of matter. temperature Contrast with depends on quantity of matter. mass and volume. Sample Problem: 1) A piece of copper has a mass of g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cm 3 ). Strategy 1. Get dimensions in common units. 2. Calculate volume in cubic centimeters. 3. Calculate the density. 6

7 Sample Problem: 2) Mercury (Hg) has a density of 13.6 g/cm 3. What is the mass of 95 ml of Hg in grams? In pounds? Solve the problem using DIMENSIONAL ANALYSIS. First, note that 1 cm 3 = 1 ml Strategy 1. Use density to calc. mass (g) from volume. 2. Convert mass (g) to mass (lb) Need to know conversion factor = 454 g / 1 lb Osmium is a very dense metal. What is its density in g/cm 3 if g of the metal occupies a volume of 2.22cm 3? a) 2.25 g/cm 3 b) 22.5 g/cm 3 c) 111 g/cm 3 Volume Displacement A solid displaces a volume of water when the solid is placed in water. 1) What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 ml to 33 ml? a) 0.2 g/ cm 3 b) 6 g/m 3 c) 252 g/cm 3 2) Which diagram represents the liquid layers in the cylinder? (K) Karo syrup (1.4 g/ml), (V) vegetable oil (0.91 g/ml,) and (W) water (1.0 g/ml) listed top to bottom: a)vwk b) WKV c) KVW 3) The density of octane, a component of gasoline, is g/ml. What is the mass, in kg, of 875 ml of octane? a) kg b) 614 kg c) 1.25 kg 4) If blood has a density of 1.05 g/ml, how many liters of blood are donated if 575 g of blood are given? a) L b) 1.25 L c) 1.83 L 7